Abstract
In our paper on matrix Möbius transformations (Comm. Algebra 9 (19) (1981), 1913–1968) we introduced the one-dimensional left-projective space over the complex n×n matrices P = P1(Mn(ℂ)). For n = 1 this space is the projective complex line P1(ℂ) and so is homeomorphic to the Riemann sphere. We studied the topology of P and the projective mappings of P onto itself. Here we present some generalizations of certain parts of the Euclidean, the spherical and the non-Euclidean geometry from the scalar to the multidimensional case.
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© 1985 Springer-Verlag
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Schwarz, B., Zaks, A. (1985). Geometries of the projective matrix space. In: Ławrynowicz, J. (eds) Seminar on Deformations. Lecture Notes in Mathematics, vol 1165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076159
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DOI: https://doi.org/10.1007/BFb0076159
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